[SOLVED] Boundary states and higher loops [Archive]

Urs Schreiber

Aug18-04, 01:16 PM

Lubos Motl

Aug19-04, 07:42 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Wed, 18 Aug 2004, Urs Schreiber wrote:\n\n> Does anyone have any references where I could find more on higher-loop\n> calculations using boundary states?\n\nI don\'t have a specific answer, but be ready that these papers do exist\nand they are relatively messy. A boundary state is a closed string state\nthat creates a boundary to the Riemann surface. A boundary is not the only\nthing that you need to create a general Riemann surface - you need handles\nand crosscaps, too.\n\nWriting the cylinder diagram as <B| exp(c.H) |B> is easy, but it clearly\nreflects the simple geometry of the cylinder. For higher genera, you will\nhave to insert "handle-creating operators" etc. Note that it is the case\nfor closed Riemann surfaces, too: a genus 2 surface can\'t be written as a\nsimple trace (like the torus) - the existence of boundaries has nothing to\ndo with this complication which already exists for purely closed string\ndiagrams.\n\nIt can apparently be done, and correct result may be obtained, but I am\nnot sure whether it is terribly helpful. Well, privately, I believe that\nsuch things could eventually be helpful in a non-perturbative covariant\nformulation of string theory - one that treats strings and D-branes on\nmore equal footing - but it is a wild enough speculation now that you\ndon\'t need to listen to me. ;-)\n\nThe matrix elements of the boundary states are only interesting for\nRiemann surfaces with two boundaries. All this alternative representation\nof the amplitudes is non-covariant as it treats different external states\ndifferently.\n\nAll the best\nLubos\n_____________________________________ _________________________________________\nE-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/\neFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)\n^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Wed, 18 Aug 2004, Urs Schreiber wrote:

> Does anyone have any references where I could find more on higher-loop
> calculations using boundary states?

I don't have a specific answer, but be ready that these papers do exist
and they are relatively messy. A boundary state is a closed string state
that creates a boundary to the Riemann surface. A boundary is not the only
thing that you need to create a general Riemann surface - you need handles
and crosscaps, too.

Writing the cylinder diagram as <B| \exp(c.H) |B> is easy, but it clearly
reflects the simple geometry of the cylinder. For higher genera, you will
have to insert "handle-creating operators" etc. Note that it is the case
for closed Riemann surfaces, too: a genus 2 surface can't be written as a
simple trace (like the torus) - the existence of boundaries has nothing to
do with this complication which already exists for purely closed string
diagrams.

It can apparently be done, and correct result may be obtained, but I am
not sure whether it is terribly helpful. Well, privately, I believe that
such things could eventually be helpful in a non-perturbative covariant
formulation of string theory - one that treats strings and D-branes on
more equal footing - but it is a wild enough speculation now that you
don't need to listen to me. ;-)

The matrix elements of the boundary states are only interesting for
Riemann surfaces with two boundaries. All this alternative representation
of the amplitudes is non-covariant as it treats different external states
differently.

All the best
Lubos
__{_______________________________________________ _____________________________}
E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^